Two spaceships in opposite direction at near c

[Dale]

The way you explain it is as if the time dilation occurs due to the further dots pacing of clockticks on the clock worldline.

He said "compared to coordinate time", which is completely correct.

Here you see clearly that the 'slowing down' of the blue and red clock have NOTHING to with the further spacing of blue or red dots relative to the black dots (red dots are equally spaced as black, blue dots are less spaced relative to the black ones!).

No, his statement is still correct. The black dots are the most closely spaced "compared to coordinate time" for black. The blue dots are further spaced and the red dots even further. "Compared to coordinate time" measures only distance normal to the lines of simultaneity, what you have labeled "spaceworld".

On a Loedel diagram (I'm now too lazy too make one) you would see that the time dilation has nothing to do with the further spacing of clock ticks on the worldline of a clock. Time dilation is about relativity of simultaneity.

This is also true, but doesn't make ghwellsjr's statements wrong. The relativity of simultaneity is what changes the meaning of "compared to coordinate time" for the different frames.

 

[Vandam]

He said "compared to coordinate time", which is completely correct.

No, his statement is still correct. The black dots are the most closely spaced "compared to coordinate time" for black. The blue dots are further spaced and the red dots even further. "Compared to coordinate time" measures only distance normal to the lines of simultaneity, what you have labeled "spaceworld".

This is also true, but doesn't make ghwellsjr's statements wrong. The relativity of simultaneity is what changes the meaning of "compared to coordinate time" for the different frames.

I only wanted to point out there was a danger of misinterpreting his diagrams and/or text because of the further spacing of the dots on the worldline, a feature of Minkowski diagrams. I never said his statements were 'wrong'. The 'further spacing of the dots relative to coordinate time' would still be valid if the spacing of the dots on the worldline would be equal. That's my point. (And that's why I prefer Loedell diagrams where possible).

 

[bobc2]

Gwelsjr,
I really appreciate your effort drawing diagrams. Good job.
Unfortunately I am not too happy with your text.
The way you explain it is as if the time dilation occurs due to the further dots pacing of clockticks on the clock worldline.
There is also a danger of interpreting your diagrams as if timedilation happens because of the taking into account of the lightbeams.
Let me put it this way:
You have drawn three different diagrams, but to see how timedilation works it is better to look at one diagram only with more information on it. I did it for you:
(For simplicity I omited what red says):
Blue notices black (and red) time dilation because when his blue clock ticks 15 (not 13 as you wrote;)), in his BLUE frame (=3D spaceworld) the black and red clock show 9.
So far so good.
Now what black says:
Black notices time dilation of blue time because "when his black clock ticks 9 seconds, IN HIS BLACK FRAME (=3D spaceworld) the blue clock is only at 5,399 sec. (9 / 1,6667).
And still IN HIS BLACK 3D world the blue 'time dilation' means: red clock is only at 1,975 sec (9 / 4,5556).
Here you see clearly that the 'slowing down' of the blue and red clock have NOTHING to with the further spacing of blue or red dots relative to the black dots (red dots are equally spaced as black, blue dots are less spaced relative to the black ones!).

On a Loedel diagram (I'm now too lazy too make one) you would see that the time dilation has nothing to do with the further spacing of clock ticks on the worldline of a clock. Time dilation is about relativity of simultaneity. (And that's only possible if you consider all events out there as observer independent entities time indications included (block universe).

Just in case you wonder what the reciprocal time dilation is for blue at 9 (see sketch below):
in blue 3D space black clock is at 5,389.
In blue 3D space when blue clock is at 5,399 the black clock is at 3,238 (= 5,399 : 1,667 ).
3D cuts through 4D block spacetime!

Very impressive insight, Vandam. I hadn't noticed that. Thanks for that observation. I think it is very good to point this out. You do a very good job of keeping the focus on the fundamental concept. Too often we get involved with the numbers and miss the underlying concept.

 

[Vandam]

That may be a little bit of an overstatement, but the intended spirit of it works fine, and you did make very good points.

Bob, I was wondering about ghwellsjr statement too...
I think we might have the same thoughts about this, but to me the whole point about the coordinate systems is that whatever coordinate system you use (apply to the outside observer independent events) then SR's 'relativity of simultaneity' shows you that reality out there is a 4D block spacetime/universe. But this is not allowed to be discussed here.

 

[ghwellsjr]

...
Gwelsjr,
I really appreciate your effort drawing diagrams. Good job.

Thanks.

Unfortunately I am not too happy with your text.

The feeling is mutual.

The way you explain it is as if the time dilation occurs due to the further dots pacing of clockticks on the clock worldline.

Time dilation occurs due to the speed of a clock in a given Inertial Reference Frame (IRF). Just as speeds of objects are different in different IRF's, so are time dilations. The time dilations for each of the space ships/stations in the three IRF's I drew are different. I illustrate the time dilation by marking off equal ticks of each observer's clock with dots along the path of each observer. I think it's a great way to explain it and I think it's very easy to see and comprehend for a newby which is what I was trying to do. Until some newbies comment about this, we'll never know if I'm right or wrong.

There is also a danger of interpreting your diagrams as if timedilation happens because of the taking into account of the lightbeams.

Are you talking about Relativistic Doppler?

Let me put it this way:
You have drawn three different diagrams, but to see how timedilation works it is better to look at one diagram only with more information on it.

I started out drawing just one diagram, not to show anything about time dilation but rather to show how light travels at c, not 2c like jartsa was promoting in post #27 as a way to explain SR to newbies. You need to read my first response to him in post #29 to understand the context of my first diagram in post #30.

I later drew two more diagrams in response to K^2's request in post #31. In each of these, the signal going from the red spaceship at his 1-minute mark is received by the black spaceship at his 9-minute mark, even though the light signal takes a varying amount of time in each IRF but still travels at c in each of them and not with respect to the speeds of the spaceships. This was the whole point of these diagrams in support of my comment to jartsa in post #29:

In an Inertial Reference Frame (IRF) in which two spaceships are traveling in opposite directions at nearly the speed of light and one of them sends a light signal to the other one, the light signal travels at c relative to the IRF, not relative to either spaceship.

(For simplicity I omited what red says):
Blue notices black (and red) time dilation because when his blue clock ticks 15 (not 13 as you wrote;)), in his BLUE frame (=3D spaceworld) the black and red clock show 9.
So far so good.

First off, I did not make a mistake with regard to 13 versus 15. I was not talking about time dilation. I was talking about how long it took for the signal to get from the red spaceship to the black spaceship at the speed of light and I said "it took over 13 minutes according to the IRF". In the other two IRF's it took 4.5 minutes and 40 minutes. Light is not time dilated. I was not talking about time dilation. Please read my comments carefully before responding to them.

And now to my main point: The blue spacestation cannot notice the black (or red) spaceship's time dilation. Time dilation is not observable by anyone anywhere anytime. It is a calculation related to the speed of an object in a given IRF. If it were ever observable, then the observer would know which arbitrary IRF we were using. Or, more significantly, if it were observable, then we could identify the an absolute ether rest state and all of Special Relativity would be out the window.

Now what black says:
Black notices time dilation of blue time because "when his black clock ticks 9 seconds, IN HIS BLACK FRAME (=3D spaceworld) the blue clock is only at 5,399 sec. (9 / 1,6667).
And still IN HIS BLACK 3D world the blue 'time dilation' means: red clock is only at 1,975 sec (9 / 4,5556).
Here you see clearly that the 'slowing down' of the blue and red clock have NOTHING to with the further spacing of blue or red dots relative to the black dots (red dots are equally spaced as black, blue dots are less spaced relative to the black ones!).

Again, the black spaceship cannot notice the time dilation of the blue spacestation for the reasons I stated before.

Just because I drew three IRF's in which one of the observer's was a rest, you should not extapolate that observer's observations to what is assigned by the IRF, such as the time dilation related to the speed of the other objects. I could just as easily have drawn another diagram in which none of the observers was a rest, for example one in which the black spaceship and the blue spacestation are traveling at the same speed in opposite directions. Then how would you explain time dilation?

On a Loedel diagram (I'm now too lazy too make one) you would see that the time dilation has nothing to do with the further spacing of clock ticks on the worldline of a clock. Time dilation is about relativity of simultaneity. (And that's only possible if you consider all events out there as observer independent entities time indications included (block universe).

Just in case you wonder what the reciprocal time dilation is for blue at 9 (see sketch below):
in blue 3D space black clock is at 5,389.
In blue 3D space when blue clock is at 5,399 the black clock is at 3,238 (= 5,399 : 1,667 ).
3D cuts through 4D block spacetime!

I wasn't wondering and I have no idea what your diagram is attempting to convey. Maybe a newby can explain it to me.

Look, the reciprocal time dilation is very easily illustrated by looking at each of the IRF's for each observer and my text succinctly states what it is. For example, in the first IRF, blue's rest frame (post #30), I state that gamma for red and black is 1.6667 and I show their dots spaced by that amount with respect to the coordinates which also happens to be with respect to blue since blue is stationary in this IRF. Then if you go to the next IRF, black's rest frame (the first small IRF in post #32), I state in the text that the time dilation for the spacestation (incorrectly identified as the spaceship) is 1.6667 and you can see the exact same spacing of the blue dots in this IRF as you do for the black dots in the first IRF. You can do the same thing for each of the other pairs of space ships/station.

 

[ghwellsjr]

Bob, I was wondering about ghwellsjr statement too...
I think we might have the same thoughts about this, but to me the whole point about the coordinate systems is that whatever coordinate system you use (apply to the outside observer independent events) then SR's 'relativity of simultaneity' shows you that reality out there is a 4D block spacetime/universe. But this is not allowed to be discussed here.

Each IRF presents a different set of coordinates for each event. The time coordinate defines simultaneity.

For example, in the first IRF (post #30), minute five for the blue spacestation is simultaneous with minute three for the black and red spaceships. However in the other two IRF's (post #32) these three events occur at different coordinate times and so are not simultaneous. But minute three for the blue spacestation is simultaneous with minute five for one or the other of the two spaceships in these other two IRF's.

What are you guys concerned with?

 

[Vandam]

Thanks.

The feeling is mutual.

Time dilation occurs due to the speed of a clock in a given Inertial Reference Frame (IRF). Just as speeds of objects are different in different IRF's, so are time dilations. The time dilations for each of the space ships/stations in the three IRF's I drew are different. I illustrate the time dilation by marking off equal ticks of each observer's clock with dots along the path of each observer. I think it's a great way to explain it

My point was: I think it is not a great way to show time dilation by stressing the fact that the dots are further spaced on the worldline (unfortunately that's a minkoski fiagram feature)
It's far more correct to explain time dilation by means which clock indication (event) pops up in a selected frame (3D space), whether the dots are spaced or not is besides the point. (That's why a loedel diagram is beter to show time dilation.)
The time dilation occurs because the worldlines take a different direction in 4D spacetime, and hence the lines of simultaneity take other directions...

and I think it's very easy to see and comprehend for a newby which is what I was trying to do. Until some newbies comment about this, we'll never know if I'm right or wrong.

Are you talking about Relativistic Doppler?

I started out drawing just one diagram, not to show anything about time dilation but rather to show how light travels at c, not 2c like jartsa was promoting in post #27 as a way to explain SR to newbies. You need to read my first response to him in post #29 to understand the context of my first diagram in post #30.

I later drew two more diagrams in response to K^2's request in post #31. In each of these, the signal going from the red spaceship at his 1-minute mark is received by the black spaceship at his 9-minute mark, even though the light signal takes a varying amount of time in each IRF but still travels at c in each of them and not with respect to the speeds of the spaceships. This was the whole point of these diagrams in support of my comment to jartsa in post #29:First off, I did not make a mistake with regard to 13 versus 15. I was not talking about time dilation.

I was talking about how long it took for the signal to get from the red spaceship to the black spaceship at the speed of light and I said "it took over 13 minutes according to the IRF". In the other two IRF's it took 4.5 minutes and 40 minutes. Light is not time dilated. I was not talking about time dilation. Please read my comments carefully before responding to them.

If you talk about gamma and showing time diltation by means of further spacing of dots on a worldline, I do not see why I may not adress the issue of time dilation.

And now to my main point: The blue spacestation cannot notice the black (or red) spaceship's time dilation. Time dilation is not observable by anyone anywhere anytime. It is a calculation related to the speed of an object in a given IRF. If it were ever observable, then the observer would know which arbitrary IRF we were using. Or, more significantly, if it were observable, then we could identify the an absolute ether rest state and all of Special Relativity would be out the window.

Time dilation is not observable?

Again, the black spaceship cannot notice the time dilation of the blue spacestation for the reasons I stated before.

Just because I drew three IRF's in which one of the observer's was a rest, you should not extapolate that observer's observations to what is assigned by the IRF, such as the time dilation related to the speed of the other objects. I could just as easily have drawn another diagram in which none of the observers was a rest, for example one in which the black spaceship and the blue spacestation are traveling at the same speed in opposite directions. Then how would you explain time dilation?

I do not get your point at all.

I wasn't wondering and I have no idea what your diagram is attempting to convey. Maybe a newby can explain it to me.

Look, the reciprocal time dilation is very easily illustrated by looking at each of the IRF's for each observer and my text succinctly states what it is. For example, in the first IRF, blue's rest frame (post #30), I state that gamma for red and black is 1.6667 and I show their dots spaced by that amount with respect to the coordinates which also happens to be with respect to blue since blue is stationary in this IRF. Then if you go to the next IRF, black's rest frame (the first small IRF in post #32), I state in the text that the time dilation for the spacestation (incorrectly identified as the spaceship) is 1.6667 and you can see the exact same spacing of the blue dots in this IRF as you do for the black dots in the first IRF. You can do the same thing for each of the other pairs of space ships/station.

Maybe it does make sense mathematically. I was thinking physics, what's out there to be measured by any coordinate systems. Maybe your diagrams are only mathematical models, mine a representation of what's out there. But I know that defending an observer independent reality is not appreciated here...

 

[bobc2]

Vandam, I feel like your point was very well placed and fully appropriate to the discussion. Not to take away from the basic point ghwells was making--that was a good response to the original post. But, you certainly brought additional valuable insight to the discussion. Your emphasis on relativity of simultaineity really needed to be presented. It's always good to put the discussion in the context of the foundational physical concepts available to us with special relativity theory.

 

[ghwellsjr]

Vandam, ... Your emphasis on relativity of simultaineity really needed to be presented. It's always good to put the discussion in the context of the foundational physical concepts available to us with special relativity theory.

Bob, why did you think there needed to be an additional emphasis on relativity of simultaneity after I explained this fully in post #41 (as if it needed any further explanation):

Each IRF presents a different set of coordinates for each event. The time coordinate defines simultaneity.

For example, in the first IRF (post #30), minute five for the blue spacestation is simultaneous with minute three for the black and red spaceships. However in the other two IRF's (post #32) these three events occur at different coordinate times and so are not simultaneous. But minute three for the blue spacestation is simultaneous with minute five for one or the other of the two spaceships in these other two IRF's.

What are you guys concerned with?

 

[bobc2]

Bob, why did you think there needed to be an additional emphasis on relativity of simultaneity after I explained this fully in post #41 (as if it needed any further explanation):

You did a good job, ghwellsjr. Your comparative time increments in the three inertial reference frames was a good direct reponse to the confusion with the 2c expressed in the earlier posts. I hope my original post reinforced the correctness of your analysis, particularly with your illustrations using the space-time diagrams. There didn't really need to be any further explanation on that point. I simply acknowledged that Vandam's additional presentation that included the hyperplanes of simultaneity was helpful as well. I think the supplemental sketches provided by Vandam, showing graphically the hyperplanes of simultaneity--with the actual time dilation values shown on the sketches, provided additional helpful information. But, again, I have no quarrel with your response to the prior posts.

Beyond that I thought perhaps you may have over emphasized the significance of the derived basis of the "measurement" of time dilation:

"And now to my main point: The blue spacestation cannot notice the black (or red) spaceship's time dilation. Time dilation is not observable by anyone anywhere anytime. It is a calculation related to the speed of an object in a given IRF. If it were ever observable, then the observer would know which arbitrary IRF we were using. Or, more significantly, if it were observable, then we could identify the an absolute ether rest state and all of Special Relativity would be out the window."

 

[bobc2]

p.s. Vandam also made the very significant observation that for the red and black guys going in opposite directions with the same relativistic speed, the spacing of the minute marks on the two time axes are the same. So, you could not use the spacings to tell you anything at all about time dilation. His emphasis of the use of the hyperplanes of simultaneity was quite appropriate. The hyperplanes of simultaneity are always different in the 4-dimensional universe for any two observers moving with respect to each other. And their space-time diagram minute mark spacings may or may not be the same, depending on the choice of charts used in the diagram. Penrose highlights this even for two observers just walking past each other (his Andromeda Paradox).

 

[ghwellsjr]

p.s. Vandam also made the very significant observation that for the red and black guys going in opposite directions with the same relativistic speed, the spacing of the minute marks on the two time axes are the same. So, you could not use the spacings to tell you anything at all about time dilation. His emphasis of the use of the hyperplanes of simultaneity was quite appropriate.

When I first read this, I was amazed that you could make such a statement. I explained how time dilation works in post #29:

...However, since the spaceships are traveling at a very high speed in the IRF, their clocks are running very slowly compared to the coordinate time of the IRF...
Think of speeds relative to an IRF, not relative to observers and you'll have no problem. ...

And I illustrated it in post #30 with further explanation:

I've drawn a diagram to show what happens in an IRF with two spaceships traveling in opposite directions at 0.8c. They both leave the blue spacestation at time 0 when they all set their clocks to 0. The dots mark off one-minute intervals for each spaceship and the spacestation. At 0.8c, gamma is 1.6667 so the dots for the spaceships are farther apart by that amount compared to the coordinate time...

So how could you say my diagram does not show anything at all about time dilation? Of course the spacing of the dots for the red and black spaceships is the same. That's because, as you said, they are traveling at the same speed and the time dilation is based on the speed.

But then it finally dawned on me. Apparently you and Vandam take the viewpoint that time dilation is calculated based on the relative speed between the clock and the observer, not between the clock and the coordinate time of the IRF.

When I said in another thread:

For example, let's say you are moving in an IRF at some high speed.

Vandam responded by saying:

You never move in your IRF. Never.

So apparently he and maybe you, believe that time dilation cannot be calculated based on the speed of an observer/clock in an IRF, correct? Is this why you said that my first graph did not show anything at all about time dilation?

 

[Vandam]

Ghwellsjr,
You show us 3 sketches but apparently have big problems of reading my sketch of post #35.
No offence, but do you know how to read a 4D Minkowski spacetime diagram?
I never said your IRF charts are wrong. But if you would be able to read your 3 charts all in one spacetime diagram only, then you would immediately see what's really going on, in 4D.

 

[ghwellsjr]

Ghwellsjr,
You show us 3 sketches but apparently have big problems of reading my sketch of post #35.
No offence, but do you know how to read a 4D Minkowski spacetime diagram?

If you are asking about diagrams promoting the block universe concept like the ones on the first page of this thread, I already gave you a thorough answer here. But if you are asking about legitimately drawn Minkowski diagrams with correct labeling (not your sketches on my graphs in post #35) which are nothing more than combining two or three IRF's like the ones I drew on this thread, then, yes, I can read those but I think they are much more difficult for a newby to understand because of the multiple axes that are combined on one chart.

I never said your IRF charts are wrong.

Then why did you feel the need to mark one of them up along with complaints about my text? If you had it to do all over again, would you have not made post #35? Will you promise to not make negative comments about my charts or explanations again, unless I make a legitimate mistake?

But if you would be able to read your 3 charts all in one spacetime diagram only, then you would immediately see what's really going on, in 4D.

This is where the problem lies. You believe that combining the information from three separate charts on to one diagram creates or reveals additional meaning about reality.

 

[K^2]

Vandam, this is a 2D problem. There is no 4D. There is one time dimension and one spatial dimension. A single diagram shows everything that's going on.

 

[Vandam]

This is where the problem lies. You believe that combining the information from three separate charts on to one diagram creates or reveals additional meaning about reality.

You simply do not get it. Of course there is more to reality than different observations (charts)!
Let me give you an analogy.
A draftsman showes you a bunch of technical drawings. Lots of sheets of paper. Two-dimensional drawings.
You say: "Awesome! 2D drawings is what architecture is about. Nothing else."
An architect has a glimp at it and says:
"The 2D drawings are fine, but... they are all 'only" sections and elevations/façades of a building. The building is reality, your 2D drawings only observations. Let me quickly sketch you the 3D perspective of the house so that you can grasp what you are working on."
Draftsman reaction: "All this 3D stuff is ridiculous.'
... Sigh.
But what then happens is even more pathetic: the more the architect explains how it all works, the more the draftsman holds tight on his 2D drawings. But that's normal behavior. Draftsmen are very good technical experts, they protect what they are good at. But they are, or become very seldom good architects.

Oh yes, sorry,... architects are probably philosophers, artistic lunatics. Isn't it?

(By the way: our two eyes capture 2D images. 2D observations. Are you going to tell me there is no 3D building out there to be observed?)

 

[ghwellsjr]

Let me give you an analogy: A movie maker hands you an old 2D movie (on film). Instead of watching the movie using a projector and a screen, you cut the film into the individual frames and then you stack them one next to the other and you claim that you have discovered the 3D reality of the movie and anyone who actually watches the movie is stuck in a 2D world.

 

[Vandam]

The difference is that I give you an explanation where the 2D drawings come from. You do not tell me where de 2D frames come from.

 

[ghwellsjr]

But your 4D block universe explanation of "reality" with regard to relativity is just a philosophical opinion. This has been explained to you and bobc2 so many times, I'm surprised you're still promoting it.

 

[K^2]

Vandam, the 4D space contains no information that's lost in a 2D section here. All of the physics of SR can be described in arbitrary N+1 space. You get identical time-dilation and space-contraction effects with absolutely identical formulae and absolutely identical explanations for any natural N. This is a 2D problem. One time and one coordinate.

 

[Dale]

Vandam, as you admitted in 37 both ghwellsjr's text and drawings are correct. The fact that they don't conform to your preferences is a matter of little consequence.

 

[ZapperZ]

Thread is starting to veer away from physics. It is now done.

Zz.